1 pointP W Smith, With those miles on the car, it could be all kinds of things that are the issue. Your best bet is to take the car to an honest independent mechanic and have him check out all of the systems. It could be bad plugs, a weak coil that breaks down when its hot, bad wiring that needs replacing, or all sorts of things that someone with experience in Camry's and ES300's can easily narrow down quickly.
1 pointThe leaking power steering oil damages the slip rings and the brushes most. These have a rubber cap and the oil from above does not go into them directly and quickly but it does go in little by little and ruins them in a month or so because the airflow is there from backside to front side. At the early stage, the resistance between the slip rings and the brushes increases and the out put voltage becomes a bit lower. You can save the alternator cleaning the inside at this stage. But if you let it go, the voltage is getting lower and lower and finally the alternator is dead and stops the function. I have seen some of those dead alternators and found that the slip rings were deteriorated.